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In induction heaters metal seems to levitate in center of radial axis, as well as longitudinal axis (see video). Is by any chance the reason for that like in this schematic, that magnetic field lines of a metal rod, forming closed loops, move in opposite direction to the coil when going around the sides of the metal? So, repulsion at the sides, and attraction along the poles. Or, is it other reason?

enter image description here

enter image description here

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    $\begingroup$ Polarity is the same. The fact that field lines are outside of the rod and inside of the wounded magnet cause the acceleration. Otherwise if there is no gap they intensify and augment each other.. sorry I mistakingly posted this comment as an answer. Had to delete it. My apologies. $\endgroup$
    – kamran
    May 13 '19 at 21:41
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    $\begingroup$ no worries. I'm just interested in having validated or falsified if there is repelling force pushing the metal piece in the induction heater towards the center of radial axis. I would assume that the repulsion along sides (acceleration), since the object is locked by attraction at poles, is acting with a vector towards center of radial axis. an analogy could be that the magnetic flux of the solenoid is squeezing its way past the magnetic flux of the iron rod, and compressing it. $\endgroup$
    – Dino
    May 13 '19 at 22:02
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    $\begingroup$ Forces will be exerted by the AC field (acting on induced circulating current I think) with any electrically conductive material, even non magnetic like Al or Cu. But you may need a particular coil shape to get a stable equilibrium for "levitation". There are more YouTube videos related to the one linked that demonstrate it. $\endgroup$
    – Pete W
    Jun 3 at 16:19
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In the clip the induced magnet into the metal creates a magnetic field opposing the coil's magnetic field and make it levitate.

In your sketch,there will be acceleration from left to right.

It could be used as a gun, hypothetically.

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    $\begingroup$ The induced magnetic field in the metal bar, does it have poles oriented in same direction as the coil magnetic field? $\endgroup$
    – Dino
    May 13 '19 at 20:28
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    $\begingroup$ Iron rod in solenoid, isn't induced field same polarity as the solenoid? $\endgroup$
    – Dino
    May 13 '19 at 20:37
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    $\begingroup$ In the schematic I assume that iron rod also follows closed loops rule. Is that accurate, or false? $\endgroup$
    – Dino
    May 13 '19 at 20:38
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    $\begingroup$ So, repulsion, accelerating left to right, I was thinking the vector would be repulsion along radial axis, and levitation along radial axis from that, like you see in the video. $\endgroup$
    – Dino
    May 13 '19 at 20:50
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    $\begingroup$ re: magnetic field opposing the coil's magnetic field, have I misunderstood that iron rod in solenoid would have poles not opposing coil magnetic field but as extension of it, same polarity? seems like electromagnet would not create stronger magnetic field otherwise if they take out one another.. $\endgroup$
    – Dino
    May 13 '19 at 20:53
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Eddy currents neutralize partially the varying magnetic field.

In electromechanical systems force affects always to the direction where smallest amount of movement causes maximal loss of field energy. There happens to be maximum loss when the heated piece is in the middle of the coil. That shouldn't surprise anyone who knows that inside a coil (which has current) there's magnetic field strength maximum in the middle. The levitation happens if the force caused by field energy reduction vs changing place happens to win the gravity.

BTW forces in DC solenoids and between permanent magnets and pieces of iron are based on the same field energy changing law but the change of the field energy occurs in AC field without magnetic materials, conductivity (+ caused eddy current) is enough.

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